Rewrite the following equation in logarithmic form. 64 = 4 3 64=4\^{ {{3}}} Rewrite the following equation in exponential form. $ \log_{49}{\left(7\right)}=\dfrac12 $
Solution: The inverse relationship of exponents and logarithms For $m>0$ and $b>0, b\neq 1$, we have the following relationship: b q = m { b\^{{ q}}}}= m if and only if $ \log_{ b }{ m}=D q$ Converting the exponential equation So 4 3 = 64 \, {{4}\^{ {3}}}}= {64}\, implies that $\,\log_{ {4}}({ {64}})=D {3}$. Converting the logarithmic equation Similarly $\, \log_{ {49}}({{7}})=\dfrac12}\,$ implies that 49 1 2 = 7 \, {49}\^{D { {\frac12}}}={7}. The logarithmic form of 64 = 4 3 64=4\^{ {{3}}} is: $\log_4 (64)={3}$ The exponential form of $\log_{49}{\left(7\right)}=\dfrac12 $ is: 49 1 2 = 7 \,49\^{{ {\frac12}}}={7}